Question

Show that the points A (0, 0), B(3, 0), C(4, 1) and D(1, 1) form a parallelogram​

Answer 1

Step-by-step explanation:

Given :-

The points A (0, 0), B(3, 0), C(4, 1) and

D(1, 1)

To find:-

Show that the points A (0, 0), B(3, 0), C(4, 1) and D(1, 1) form a parallelogram

Solution:-

Given points are A (0, 0), B(3, 0), C(4, 1) and D(1, 1)

We know that

In a Parallelogram , The diagonals bisect to each other .

=> Mid Point of AC = Mid Point of BD

To find the given points are the vertices of a Parallelogram then we have to show that

Mid Point of AC = Mid Point of BD

We know that

The mid point of a line segment joining the points (x1, y1) and(x2, y2) is

[(x1+x2)/2 , (y1+y2)/2]

Mid Point of AC :-

Let (x1, y1)= A (0, 0)=>x1=0 and y1 = 0

Let (x2, y2)=C(4, 1)=>x2=4 and y2=1

Mid Point of AC

=>[(0+4)/2, (0+1)/2]

=> (4/2,1/2)

=>(2,1/2)

Mid Point of AC = (2 , 1/2)----------(1)

Mid Point of BD:-

Let (x1, y1)=B(3, 0) =>x1=3 and y1 = 0

Let (x2, y2)= D(1, 1)=>x2=1and y2=1

Mid Point of AC

=>[(3+1)/2, (0+1)/2]

=> (4/2,1/2)

=>(2,1/2)

Mid Point of BD= (2 , 1/2)----------(2)

From (1)&(2)

Mid Point of AC = Mid Point of BD

So Given points are the vertices of the Parallelogram

Answer:-

The points A (0, 0), B(3, 0), C(4, 1) and D(1, 1) form a parallelogram

Used formula:-

• In a Parallelogram , The diagonals bisect to each other .

• The mid point of a line segment joining the points (x1, y1) and(x2, y2) is
• [(x1+x2)/2 , (y1+y2)/2]